qanda-logo
search-icon
Symbol

Calculator search results

Calculate the integral value
Answer
circle-check-icon
expand-arrow-icon
expand-arrow-icon
expand-arrow-icon
expand-arrow-icon
$5$
Calculate the integral value
$\color{#FF6800}{\int _{0} ^{1}{(4x - 1) ^ {3}}dx}$
$ $ To solve for the definite integral, first calculate the indefinite integral $ $
$\color{#FF6800}{\int (4x - 1) ^ {3}dx}$
$\color{#FF6800}{\int (4x - 1) ^ {3}dx}$
$ $ Substitute $ t = 4x - 1 $ to simplify integral calculation $ $
$\color{#FF6800}{\int \dfrac {t ^ {3}} {4}dt}$
$\color{#FF6800}{\int \dfrac {t ^ {3}} {4}dt}$
$ $ Utilize integration $ \int a \times f(x)dx = a \times \int f(x)dx, a \in ℝ $ $ $
$\color{#FF6800}{\dfrac {1} {4} \times \int t ^ {3}dt}$
$\dfrac {1} {4} \times \color{#FF6800}{\int t ^ {3}dt}$
$ $ Using $ \int x ^ {n}dx = \dfrac {x ^ {n + 1}} {n + 1}, n \neq - 1 $ , calculate the integral $ $
$\dfrac {1} {4} \times \color{#FF6800}{\dfrac {t ^ {4}} {4}}$
$\dfrac {1} {4} \times \dfrac {\color{#FF6800}{t} ^ {4}} {4}$
$ $ Change the substituted $ t = 4x - 1 $ again $ $
$\dfrac {1} {4} \times \dfrac {\color{#FF6800}{(4x - 1)} ^ {4}} {4}$
$\color{#FF6800}{\dfrac {1} {4} \times \dfrac {(4x - 1) ^ {4}} {4}}$
$ $ Multiply the fractions $ $
$\color{#FF6800}{\dfrac {(4x - 1) ^ {4}} {16}}$
$\color{#FF6800}{\dfrac {(4x - 1) ^ {4}} {16}}$
$ $ Rewrite the interval of definite integral $ $
$\color{#FF6800}{\dfrac {(4x - 1) ^ {4}} {16} |_{0}^{1}}$
$\color{#FF6800}{\dfrac {(4x - 1) ^ {4}} {16} |_{0}^{1}}$
$ $ Use $ f(x) |_{a}^{b} = F(b) - F(a) $ to calculate the formula $ $
$\color{#FF6800}{\dfrac {(4 \times 1 - 1) ^ {4}} {16} - \dfrac {(4 \times 0 - 1) ^ {4}} {16}}$
$\color{#FF6800}{\dfrac {(4 \times 1 - 1) ^ {4}} {16} - \dfrac {(4 \times 0 - 1) ^ {4}} {16}}$
$ $ Calculate the value $ $
$\color{#FF6800}{5}$
Solution search results
Have you found the solution you wanted?
Try again
Try more features at Qanda!
check-iconSearch by problem image
check-iconAsk 1:1 question to TOP class teachers
check-iconAI recommend problems and video lecture